The Mole

Editor: Drew Humphrey

The mole is a unit of measurement used in chemistry to express amounts of a chemical substance, defined as an amount of a substance that contains as many elementary entities(e.g., atoms, molecules, ions, electrons) as there are atoms in 12 grams of pure carbon-12 (12C), the isotope of carbon with atomic weight 12. This corresponds to a value of6.02214179(30)×1023 elementary entities of the substance. It is one of the base units in the International System of Units, and has the unit symbol mol.

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Group 1: pgs. 287-296

MEASURING MATTER

pgs. 287-288 by Freddy Dwyer

• We live in a quantitative world, NUMBERS RULE everything.
• Scientists constantly depend on numbers and measurement to explain or discover new formulas. Without numbers the world would not be able to exist.
• Numbers can be viewed as the universal language.

WAYS TO MEASURE MATTER

• Counting- 1,2.3 etc... Or "I bought a 6 pack of soda"
• Mass- "I bought a pound of potatoes"
• Volume- " I bought 2 Liters of soda"

For example if apples were to be used. One could buy apples by count equaling 12
by count: 1 dozen apples= 12 apples
by mass: 1 dozen apples= 2.0 kg apples
by volume: 1 dozen apples= 0.20 bushel apples

THESE ALL EQUAL THE SAME AMOUNT YET ARE DIFFERENT MEASUREMENTS.

Finding Mass from a Count

Pg. 289 Lauren Rossi

example problem:
What is the mass of 90 average-sized apples if 1 dozen of the apples has a mass of 2.0 kg?

1. Analyze
   • list the known and the unknown
     • Known: number of apples=90
       • 12 apples=1 dozen apples
       • 1 dozen apples=2.00 kg apples
     • Unknown: mass of 90 apples=?kg

You can use dimentional analysis to convert the number of apples to the mass of apples. Carry out this conversion by performing the following sequence of conversions:
Number of apples ---> Dozens of apples ---> mass of apples

1. Calculate
   • Solve for the unknown
     • the first conversion factor is
     • the second conversion factor is
     • multiplying the original number of apples by these two conversion factors gives the answer in kilograms.
     • the mass of 90 average-sized apples is 15 kg.
2. Evaluate
   • Does the result make sense?
     • Because a dozen apples has a mass of 2.0 kg, and 90 apples is less than 10 dozen apples, the mass should be less than 20 kg of apples.
     • (10 dozen X 2.0 kg/dozen)

Representative Particles

Page 290 by Matt McKeon

• The term Representative Paticle refers to the species present

in a substance(atoms, molecules, or formula units)

• The representative particle of most elements is the atom
• Iron is composed of Iron atoms, Helium is composed

of helium atoms.

• Seven elements however exist as diatomic particles

(H, N, O, F, Cl, Br and I)

• The representative particles of all molecular compounds is the molecule
• For Ionic compounds th representative particle is the formula unit CaCl

Converting Number of Particles to Moles

• The relationship,1 mol=6.02x1023Representative Particles,

is the basis for a conversion factor that you can use to convert numbers

of representative particles to moles.




http://www.youtube.com/watch?v=21tLXgeYALc (Ctrl+click)

Converting Number of Atoms to Moles

Page 291 Lauren Rossi

example problem:
Magnesium is a light metal used in the manufacture of aircraft, automobile wheels, tools,and garden furniture. How many moles of magnesium is 1.25 X 10^23 atoms of magnesium?

1. Analize
   • List the knowns and the unknown.
     • Known: number of atoms= 1.25 X10^23 atoms Mg
       • 1 mol Mg= 6.02 X 10^23 atoms of Mg
       • the desired conversion is atoms ---> moles
     • Unknown: moles= ? mol Mg
2. Calculate
   • solve for the unknown
     • the conversion factor is
     • multiplying atoms of Mg by the conversion factor gives the answer
3. Evaluate
   • Does the result make sense?
     • Because the given number of atoms is less than one-fourth of Avogadro's number, the answer should be less than one-fourth mole of atoms. The answer should have three significant figures.

Converting Moles to Number of Particles

Pg 291-292 by Pat Hodge

To convert moles to number of particles, the student must know how many atoms are in a representative particle of the compound.
This is determined by the chemical formula.
1 Mole= 6.02 X 10^23
representative particles= moles X 6.02 X 10^23 representative particles/ 1 mole
http://www.youtube.com/watch?v=kJQnOVk8k2A

The Mass of a Mole of an Element

pages 293-295 by Matt Moschella

• the average carbon with an atomic mass of 12.0 amu is 12 times heavier than an average hydrogen atom with an atomic mass of1.0 amu. therefore n carbon atoms will always be 12 times heavier than n hydrogen atoms.

..............CarbonAtoms..................

..........HydrogenAtoms................

............MassRatio.............

Number	Mass(amu)	Number	Mass(amu)	MassCarbon/MassHydrogen
1	12	1	1	12amu/1amu=12/1
2	24	2	2	24amu/2amu=12/1
10	120	10	10	120amu/10amu=12/1
Avogadro'snumber	(6.02x1023)x(12)	Avogardo'snumber	(6.02x1023)x(1)	(6.02x1023)x(12)/ (6.02x1023)x(1)=12/1

• the atomic mass of an element in the periodic table in not a whole number.
• The atomic mass of an element expressed in grams is the mass of a mole of the element.
• the mass of a mole of an element is called the Molar Mass.
• often the molar mass will be rounded (in the book it is rounded to the nearest decimal point).
• also, 12.0 grams of carbon and 16.0 grams of oxygen contain the same number of atoms because the molar mass of two elements must contain the same amount of atoms.
• for every mole of any element there are 6.02x1023 atoms of that element.

example:
you have 24grams of carbon, how many atoms of carbon do you have?
1. find carbon on the periodic table:

2. the atomic mass of carbon is about 12 amu. because you have twice the amus of one carbon you must have two moles of carbon (12 grams of carbon per mole)
3. because there are 6.02x1023 atoms for one mole, multiply it by two to get the number of atoms for two moles. 2x(6.02x1023)=1204000000000000000000000 atoms or 1.204x10^24.

The Mass of a Mole of a Compound
Page 295 By Abby Williams

• to be able to find the mole of a compound, you need to know the compounds formula
• add the atomic masses of the atoms that make up the molecule
• the molar mass of any compound is the mass in grams of 1 mole of the compound
• to calculate the molar mass of a compound, find the number of grams of each element in one mole of the compound
• add the masses of the elements in the compound

Finding the Molar Mass
page 296 by kelsey persechini

• 
  

http://www.youtube.com/watch?v=oA4Y8EQlkz0

• To find the molar mass of a compound
• 1st write it out as a symbol ( H2O)
• 2nd break it up into each individual compound ( make sure to make note of how much of that element is )
• 3rd find mass of element (oxygen is 16)
• 4th multiply the mass of the element by the amount of that element in the compound
• 5th add all the masses of the individual elements togeather to get the molar mass

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Group 2: pgs. 297- 304


The Mole-Mass Relationship (pg. 297 by Andrew Marcotte)

-the molar mass of any substance is the mass in grams of one mole of that substance
-this applies to ALL substances - elements, molecular compounds, and ionic compounds
-HOW WOULD YOU ANSWER WHAT THE MOLAR MASS OF OXYGEN IS?
-assume it is molecular oxygen (O2)
-the molar mass is 32.0 grams (2x16.0g)

Use the molar mass of an element/compound to convert between the MASS of a substance and the MOLES of a substance.

CONVERTING MOLES TO MASS ( pg. 298 by Alex Ortiz)

1. Analyze

• list the known and the unknown
• the mass of the compound is calculated from the known number of moles of the compound. The desired conversion is moles------>mass.

2.Calculate

• solve for the unknown
• Multiply the given number of moles by the conversion factor relating moles to grams

3. Evaluate

• does the answer make sense?
• the answer will be rounded to the correct number of significant figures.

Converting Mass to Moles (pg. 299 by Emily Healy)

moles=mass(grams) * 1mol/ mass(grams)

• Analyze

  • list the known and unknown
  • known= the mass
  • Unknown=number of moles

• Calculate

  • solve for the unknown
  • multiply the given mass by the conversion factor relating mass to moles.

• evaluate

  • does the result make sense?
  • if the given mass is slightly larger then the mass of one half the mole then the answer should be slightly larger then one half a mole.

Katie Manis
http://www.youtube.com/watch?v=VAyGe_fW3FE&feature=player_detailpage

The Mole – Volume Relationship (pg. 300 by Monika Maczuga)

• The volumes of one mole of different solid and liquid substances are NOT the same.

Example: The volumes of one mole of glucose (blood sugar) and one mole of paradichlorobenzene (moth crystals) are much larger than the volume of one mole of water.

• However, unlike liquids and solids, the volumes of moles of gases measured under the same physical conditions are more predictable.

Avogadro’s Contribution

• In 1811, Amedeo Avogadro proposed a groundbreaking explanation.

Avogadro’s Hypothesis – states that equal volumes of gases at the same temperature and pressure contain equal numbers of particles.

• Particles that make up different gases are not the same size.
• Gas particles are so far apart that a collection of relatively large particles do not require more space than the same number of relatively small particles.
• Large expanses of space exist between individual particles of gas.
• The volume of a gas varies with a change in temperature

Example: You buy a balloon filled with helium and take it home on a cold day. You may notice that the balloon shrinks while it is outside. Higher ---> Lower Temperature



The volume of a gas also varies with a change in pressure
Example: The increase in pressure when a plane lands causes the volume of the of the air in the bottle to decrease. The trapped air occupied the full volume of the bottle in the cabin where the air pressure was lower. Lower ---> Higher

• Because of these variations, the volume of gas is measured at a standard temperature and pressure.

Standard Temperature and Pressure (STP) – a temperature of 0°C and a pressure of 101.3 kPa or 1 atmosphere (atm)
v At STP, 1 mole or 6.02 x 10^23 representative particles, of any gas occupies a volume of 22.4 L.

v The quantity, 22.4 L, is called the molar volume of a gas.

Calculating Volume at STP (pg. 301 Lindsey Trafford)

• the molar volume is used to convert a known number of molecules of gas to the volume of the gas at STP

• 22.4 L = 1 mol at STP

- volume of gas = moles of gas X 22.4L/ 1mol

1. example: volume of O2 0.375 mol X 22.4L/ 1 mol 8.40 L

• opposite conversion uses the same relationship( 22.4 L = 1 mol at STP)

- opposite conversion is from the volume of gas at STP to the number of molecules of gas

2. example: moles = 0.200 L H2 x 1 mol H2/ 22.4 L H2 = 8.93 x 10-1 mol H23

The Mole Road Map

The mole is at the center of your chemical calculations and is used to convert one unit to another. The map shows the conversion factors needed to convert with volume, mass, and number of particles

Page 302 by Sejal Batra

Calculating Molar Mass from Density

Different gasses have different densities. Usually the density of a gas is measured in grams per liter and at a specific temperature. The density of a gas at STP and the molar volume at STP (22.4 L/mol) can be used to calculate the molar mass of the gas.

Molar mass= density at STPXmolar volume at STP

page 303 Chris Delude

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Group 3: pgs. 305- 312

Videos by Sean Doherty
The Percent Composition of a Compound (p. 305) -- Nathaniel Gallishaw
-- It is important to know the "relative amount" of each component of a mixture or compound.
-- The "relative amounts" of elements in a compound are expressed through percent composition.
-- This is based on the mass of each element in the compound and expressed as a percent.
-- In the compound K2CrO4 the percent composition of each element is:
K = 40.3% Cr = 26.8% O = 32.9% (percentages must add up to 100%)
-- Use this formula for percent composition: % mass of element = (mass of element / mass of compound) x 100%

Kevin Petterson (pgs. 305-306)
Percent Composition from Mass Data:
Sample Problem:

• When a 13.60 g sample of a compound containing only magnesium and oxygen is decomposed, 5.40 g of oxygen is obtained. What is the percent composition of this compound?
  • Step 1: Analyze- List the knowns and the unknown

Knowns:

• mass of compound = 13.60 g
• mass of oxygen = 5.40 g
• mass of magnesium = 13.60 g - 5.40 g = 8.20 g Mg

Unknowns:

• percent of Mg = ? % Mg
• percent of O = ? % O
  • The percent by mass of an element in a compound is the mass of that element divided by the mass of the compound multiplied by 100%

• Step 2: Calculate- Solve for the unknown

• % of Mg = (mass of Mg / mass of compound) x 100%
  • Ex: (8.20g / 13.60g) x 100% = 60.3

• % of O = (mass of O / mass of compound) x 100%
  • Ex: (5.40g / 13.60g) x 100% = 39.7%

• Step 3: Evaluate- Does the result make sense?
  • The percents of the elements must add up to 100%
    • Ex: 60.3% + 39.7% = 100%

Practice problems:
1. A compound is formed when 9.03g Mg combines completely with 3.48g N. What is the percent composition of this compound?
2. When a 14.2g sample of Mercury (II) Oxide is decomposed into its elements by heating, 13.2g Hg is obtained. What is the percent composition of the compound?

Percent Composition from the Chemical Formula

[Joe Geraghty]

Calculate the percent by mass of each element by dividing the mass of that element
in one mole of the compound by the molar mass of the compound and multiplying by 100%.

% mass = mass of element in 1 mol compound / molar mass of compound x 100%

The percents of the elements add up to 100% when the answers are expressed to two significant figures.

Practice Problems:
Calculate the percent composition of these compounds: ethane and sodium hydrogen sulfate.
Calculate the percent nitrogen in these common fertilizers: NH3 and NH4NO3

Percent Composition as a Conversion Factor (Emily Mills)

- used to calculate the number of grams of any element in a specific mass of a compound.

Multiply the mass of the compound by a conversion factor based on the percent composition of the
element in the compound.

Here is an example:

How much carbon and hydrogen are contained in 82.0 g of propane?
82.0 g C3H8 x 81.8 g C / 100 g C3H8 = 67.1 g C
82.0 g C3H8 x 18 g H / 100 g C3H8 = 15 g H
The sum of the two masses equals 82 g C3H8.

Percent Composition from the Chemical Formulas

Empirical Formula

Michael Clarke

In chemistry, the empirical formula of a chemical compound is the simplest positive integer ratio of atoms of each element present in a compound. An empirical formula makes no reference to isomerism, structure, or absolute number of atoms. The empirical formula is used as standard for most ionic compounds, such as CaCl2, and for macromolecules, such as SiO2.



Empirical formula is in the smallest whole number ratio.

Molecular Formulas Pg. 311 Andrew Whalen

• The molecular formula of a compound is either the same as its experimentally determined empirical formula, or it is a simple whole-number multiple of its empirical formula
• Once you have determined the empirical formula of your newly synthesized compound, you can determine its molecular formula, but you must know the compound's molar mass
• A chemist often uses an instrument called a mass spectrometer to determine molar mass
• The compound is broken into charged fragments (ions) that ravel through a magnetic field
• The magnetic field deflects the particles from their straight-line paths
• The mass of the compound is determined from the amounts of deflection experienced by the particles
• From the empirical formula, you can calculate the empirical formula mass (efm)
• This is the molar mass represented by the empirical formula
• Then you can divide the experimentally determined molar mass by the empirical formula mass
• This gives the number of empirical formula units in a molecule of the compound and is the multiplier to convert the empirical formula to the molecular formula